3. 11-4: An article in Technometrics by S. C. Narula and J. F. Wellington [āPrediction, Linear Regression, and a Minimum Sum of Relative Errorsā (Vol. 19, 1977)] presents data on the selling price and annual taxes for 24 houses. The data are shown in the following table.
Sale Price/100 | Taxes (Local, School, County)/1000 | Sale Price/100 | Taxes (Local, School, County)/1000
25.9 | 4.9176 | 30.0 | 5.0500
29.5 | 5.0208 | 36.9 | 8.2464
27.9 | 4.5429 | 41.9 | 6.6969
25.9 | 4.5573 | 40.5 | 7.7841
29.9 | 5.0597 | 43.9 | 9.0384
29.9 | 3.8910 | 37.5 | 5.9894
30.9 | 5.898 | 37.9 | 7.5422
28.9 | 5.6039 | 44.5 | 8.7951
35.9 | 5.8282 | 37.9 | 6.0831
31.5 | 5.3003 | 38.9 | 8.3607
31.0 | 6.2712 | 36.9 | 8.1400
30.9 | 5.9592 | 45.8 | 9.1416
(a) Assuming that a simple linear regression model is appropriate, obtain the least squares fit relating selling price to taxes paid. What is the estimate of ĻĀ²?
(b) Find the mean selling price given that the taxes paid are x = 7.30.
(c) Calculate the fitted value of y corresponding to x = 5.6039. Find the corresponding residual.
(d) Calculate the fitted yĢįµ¢ for each value of xįµ¢ used to fit the model. Then construct a graph of yĢįµ¢ versus the corresponding observed value yįµ¢ and comment on what this plot would look like if the relationship between y and x was a deterministic (no random error) straight line. Does the plot actually obtained indicate that taxes paid is an effective regressor variable in predicting selling price?